Question: Reduce to lowest terms: $- \dfrac{9}{8} \div - \dfrac{7}{6} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{7}{6}$ is $- \dfrac{6}{7}$ Therefore: $ - \dfrac{9}{8} \div - \dfrac{7}{6} = - \dfrac{9}{8} \times - \dfrac{6}{7} $ $ \phantom{- \dfrac{9}{8} \times - \dfrac{6}{7}} = \dfrac{-9 \times -6}{8 \times 7} $ $ \phantom{- \dfrac{9}{8} \times - \dfrac{6}{7}} = \dfrac{54}{56} $ The numerator and denominator have a common divisor of $2$, so we can simplify: $ \dfrac{54}{56} = \dfrac{54 \div 2}{56 \div 2} = \dfrac{27}{28} $